Introducing phase jump tracking -- a fast method for eigenvalue evaluation of the direct Zakharov-Shabat problem
Numerical Analysis
2021-02-24 v2 Numerical Analysis
Exactly Solvable and Integrable Systems
Abstract
We propose a new method for finding discrete eigenvalues for the direct Zakharov-Shabat problem, based on moving in the complex plane along the argument jumps of the function , the localization of which does not require great accuracy. It allows to find all discrete eigenvalues taking into account their multiplicity faster than matrix methods and contour integrals. The method shows significant advantage over other methods when calculating a large discrete spectrum, both in speed and accuracy.
Cite
@article{arxiv.2003.02215,
title = {Introducing phase jump tracking -- a fast method for eigenvalue evaluation of the direct Zakharov-Shabat problem},
author = {Igor Chekhovskoy and Sergey Medvedev and Irina Vaseva and Egor Sedov and Mikhail Fedoruk},
journal= {arXiv preprint arXiv:2003.02215},
year = {2021}
}